The MareyMap package version 1.3
Aurélie Siberchicot, Clément Rezvoy, Delphine Charif,
Laurent Guéguen and Gabriel Marais
November 14, 2016
MareyMap is an R package to estimate local recombination rates along the genome. MareyMap relies on
comparing the genetic and the physical maps of a given chromosome to estimate local recombination
rates (given by the slope of the curve describing the relationship between both variables), a graphical
method called the Marey map method introduced by A. Chakravarti in 19911 . MareyMap accepts Marey
map data as input (genetic and physical positions of markers for a set of chromosomes of a species) and
will return local recombination rate estimates.
MareyMap has many features and possible options (detailled in the present user guideline document)
including:
• taking Marey map data from any species, including some Marey map data for a few species provided
with the package
• estimating local recombination rates using different interpolation methods
• providing in an automatic way local recombination rates for any given gene (or set of genes) in the
genome
If you use MareyMap, please cite:
Rezvoy C, Charif D, Guéguen L, Marais GAB. (2007) MareyMap: an R-based tool with graphical
interface for estimating recombination rates. Bioinformatics 23(16):2188-9.
Contents
1 Installing and starting MareyMap
1.1 Initial installation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 Starting MareyMap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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2 Data
2.1 Loading data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Map cleaning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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3 Interpolation methods
3.1 Selecting and running an interpolation method .
3.1.1 Selecting a method . . . . . . . . . . . . .
3.1.2 Changing and deleting interpolations . . .
3.1.3 Common parameters . . . . . . . . . . . .
3.1.4 Running a method to every map in a set .
3.2 Available interpolation methods . . . . . . . . . .
3.2.1 Loess . . . . . . . . . . . . . . . . . . . .
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1 Chakravarti
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A. (1991) A graphical representation of genetic and physical maps: the Marey map. Genomics 11(1):219-
22.
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3.2.2
3.2.3
Sliding window . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Cubic splines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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4 Queries
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5 Saving your results
5.1 Saving data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 Exporting pictures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3 Loading previous analyses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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1
Installing and starting MareyMap
1.1
Initial installation
MareyMap is a package developed under the R software; sources are available on http://cran.r-project.
org/. The R software must be installed in such a way that graphical interfaces can work. On Windows
and Mac OS, this is automatically done when the R software is installed. On Linux, the two libraries tcl
and tk must be installed, which is done by installing R with the --with-tcltk option.
When R is installed, the package MareyMap and its dependencies tcltk, tkrplot and tools must be
installed, using the commands
install.packages(MareyMap)
install.packages(tcltk)
install.packages(tkrplot)
install.packages(tools)
on a R console.
1.2
Starting MareyMap
In a R console, first load the package:
library(MareyMap)
Then, open a graphical interface with the command:
startMareyMapGUI()
A new window, as shown in Figure 1 should open. If not, close your R console, re-load and re-start the
package.
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Figure 1: The MareyMap graphical interface
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2.1
Data
Loading data
The user must either choose at least one dataset among those available in the MareyMap package or
import his/her own dataset.
6 ready-to-use datasets are provided along with the package. This includes Marey maps for: Arabidopsis thaliana 2 , Caenorhabditis elegans 3 , Drosophila melanogaster 4 and Homo sapiens 5 (male, female and
sex-averaged).
When the input dataset does not come from the package, the extension of the data file must be txt, rda,
Rda, rdata or Rdata. When using a text file, the input data must be a data frame with the columns
“set”, “map”, “mkr”, “phys” and “gen”. If missing, an additional column “vld” (indicating if the marker
is valid or not) is added with TRUE value by default. Column names must be in the first row and values
must be separated by space or tab.
Choose and open a dataset with the “File” and “Open” menus. The “Data” menu lists all the dataset
opened. When one dataset is selected, the “MAPS” left frame is updated and shows the Marey maps
(one for each chromosome) available in the dataset.
2 Wright SI, Agrawal N, Bureau TE. Effects of recombination rate and gene density on transposable element distributions
in Arabidopsis thaliana. Genome Res. 2003. 13:1897-1903.
3 Wormbase Release WS160 http://www.wormbase.org. see Rizzon C, Martin E, Marais G, Duret L, Segalat L, Biemont
C. Patterns of selection against transposons inferred from the distribution of Tc1, Tc3 and Tc5 insertions in the mut-7 line
of the nematode Caenorhabditis elegans. Genetics. 2003. 165:1127-1135.
4 Marais G, Piganeau G. Hill-Robertson interference is a minor determinant of variations in codon bias across Drosophila
melanogaster and Caenorhabditis elegans genomes. Mol Biol Evol. 2002. 19:1399-1406.
5 Rutgers Combined Linkage-Physical Maps, version 2.0 (Build 35). Xiangyang Kong and Tara Matise 12/08/2004. see
Kong et al. A high-resolution recombination map of the human genome. Nat Genet. 2002. 31:241-247.
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In the “MAPS” frame, the user selects one map (i.e. one chromosome) by clicking on it. The selected
map is displayed (the physical positions on x-axis and the genetic distances on y-axis) in the central
part of the interface. The “INTERPOLATIONS” right frame becomes active and the user can perform
interpolations. Figure 2 shows the Arabidopsis thaliana Chromosome 1 Marey map as example.
Figure 2: Displayed Marey map of a chromosome
2.2
Map cleaning
Physical or genetic maps occasionally include errors. Those will appear as outliers in a Marey map of a
chromosome, disrupting the monotonically increasing behaviour expected from a Marey map function.
Clicking on a marker on the map (the point becomes filled red) will display information about this marker
in the “MARKER” left frame. If you un-select the “Valid” option (a red cross covers the point), this
marker will not be included in the interpolations. This operation is reversible.
Deleting the marker is also possible. The marker will be removed from the rest of the analysis, but not
from the raw data. The marker will be included again if the dataset is re-uploaded.
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3.1
3.1.1
Interpolation methods
Selecting and running an interpolation method
Selecting a method
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To run an interpolation method on a Marey map,
click on the
icon in the “INTERPOLATIONS”
right frame and select an interpolation method from
the list (see Figure 3).
After interpolation is done, the results are displayed
in the central frame.
Figure 3: List of interpolation methods.
3.1.2
Changing and deleting interpolations
You can change the parameters of an interpolation by clicking on the
frame and delete an interpolation by clicking on the
icon in the “INTERPOLATIONS”
icon. Interpolations can be shown in the central
displaying frame, using the
checkbox. The
checkbox indicates whether the interpolation results
should be included when saving the results into a text file.
3.1.3
Common parameters
Some parameters are common for all interpolation methods. By default, a name (“Name” parameter) is given to an interpolation (can be changed by the user), the interpolation results will be saved
(“Saved” parameter) and displayed (“Displayed” parameter), and a line color (“Line color” parameter)
is automatically chosen. These parameters can be changed at any time.
See 3.2 for specific parameters to each interpolation method.
3.1.4
Running a method to every map in a set
It is possible to run the same interpolation method (with the same parameters) on all the Marey maps
(all the chromosomes) of a dataset. Just click on the “Apply to every map in the set” checkbox in the
window that opens when a new interpolation is being set (see Figure 3). In this case, the interpolation
will have the same name for all the Marey maps.
Similarly, changing or deleting an interpolation will affect all the maps if you use the “Apply to every
map in the set” checkbox.
3.2
Available interpolation methods
The MareyMap package currently provides three interpolation methods: Loess, Sliding Windows and
Cubic Splines.
3.2.1
Loess
Loess (or Lowess for LOcally WEighted Scatterplot Smoothing) estimates the recombination rates by
locally adjusting a polynomial curve (1st or 2nd degree). The size of the window is defined as a percentage
of the total number of markers and therefore can adapt to the variation of the density of markers across
the map. Inside of a given window, each marker is attributed a weight depending on how far they are
from the center of the window. The parameters β of the curves are those that minimize the mean squared
deviation between the data and the curve:
Pn
Q = i=1 ωi [yi − f (xi , β̂)]2
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where (xi , yi ) are the observed data and ωi is the weight of each marker calculated by:
ω(u) = (1 − u3 )3
with:
u=
|x0 −xi |
maxN (x0 )|x0 −xi |
For this method, you can select the degree of the fitted curve (“Degree” parameter) and the size of the
window (“Span” parameter). The span parameter is the percentage of the total number of points to take
into account for computing the local polynomial at the vicinity of a marker. Span controls the degree
of smoothing. The same span value is applied to all the maps, which may not be optimal if the error
variance or the curvature of the underlying function f varies.
This method is based on the R loess function. For
more information about this method, write ?loess
in a R console.
Selecting this method will open a window as shown
in Figure 4.
Figure 4: The Loess method
3.2.2
Sliding window
This method estimates the local recombination
rates by carrying out linear regressions within a
sliding window of a given physical size. You may
adjust the size of the window (“Size” parameter), the distance between two successive windows
(“Shift” parameter), as well the minimum number
of marker per window for the interpolation to be
carried out (“Threshold” parameter).
Selecting this method will open a window as shown
in Figure 5.
Figure 5: The sliding window method
3.2.3
Cubic splines
A cubic smoothing spline behaves approximately like a kernel smoother, but it corresponds to the function
fˆ that minimizes the penalized residual sum of squares given by:
R
Pn
P RSS = i=1 (yi − f (xi ))2 + λ (f ′′ (t))2 dt
λ is the smoothing parameter, corresponding to the span in loess. A different λ can be specified using
the “Spar” parameter.
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The “Degree of freedom” parameter controls the amount of smoothing and corresponds to the trace
of the smoothing matrix. It is also estimated automatically using spar or by cross-validation.
These two parameters will be estimated automatically under R either by locally or generalized crossvalidation.
The generalized cross-validation is performed using this function:
Pn
CV (λ) = n1 i=1 (yi∗ − fˆλ−i (xi ))
Here fˆλ−i (xi ) is the leave-one-out smooth at xi , that is constructed using all the data except for (xi , yi )
and then the resulting least squares line is evaluated at xi . CV is calculated for different values of λ and
the λ that minimizes this criterion is chosen. The “Generalized cross-validation” method should be
used when there are several markers with identical physical position.
In the graphical interface, you must fill the parameter chosen in the “Type” list.
This method is directly based on the function
smooth.spline of R. To get more information
about this method you can type ?smooth.spline
in a R console.
Selecting this method will open a window as shown
in Figure 6.
Figure 6: The cubic splines method
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Queries
Once an interpolation method has been run on a map, you can make queries about local recombination
rates using the “LOCAL RECOMBINATION RATE” right frame. There are four different ways of using
this frame.
1. You may want to know the recombination rate at a given physical position on the currently displayed
map. The position must be specified in base pair (ex. 31564623) but can also be expressed using Mb or
Kb (ex. 31Mb, 564Kb or even 31Mb+564Kb+623). The local recombination rate from each interpolation
available will be provided for this position. This is done when the “Query” button is pressed, and shown
in the updated “LOCAL RECOMBINATION RATE” window. A vertical red line is then displayed on
the two central graphics, at the physical position of interest.
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2. You may want to know the recombination
rate at several positions on the currently displayed
map. Just list them separating them by ”:” (ex.
31Mb:12287456:44Kb+564). When clicking on the
“Query” button, results will be displayed in a separate window (see Figure 7) and can be saved into
a text file. The results will include one column per
interpolation available for the displayed map.
Figure 7: Example of output for several queries.
3. You may want to know the recombination rate at many positions (for instance all the genes of a
genome). This can be done by up-loading a text file including all the positions. To do this, you can
• enter the path of the above mentioned file and click on the “Query” button,
• or click on “Read positions from file” and select the file using the file selector dialog window.
The input file must be a text file (txt extension) containing at least a “map” column and a “phys” column
indicating respectively the map and the physical position of each gene. An example file test query.txt is
provided along with the package. This file may also include a “set” column if there are genes from several
genomes for instance (if this column is not present all the genes are considered from the same genome,
i.e. the same query). Any other column will be ignored by the program but will be kept in the output file.
4. It is also possible to know the recombination rate at a position in an interactive way. When one marker
is selected (by clicking) on the displayed map (in the top central frame), some details are updated in the
“MARKERS” left frame. You will be able to click on the “Query recombination rate” button. As
before, results are shown in the updated “LOCAL RECOMBINATION RATE” frame and a vertical red
line is displayed on the two central graphics, at the physical position of interest (see Figure 8).
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Figure 8: Example of an interactive query.
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5.1
Saving your results
Saving data
Maps can be saved to R data files (rda, Rda, rdata or Rdata) or to text files (txt).
All interpolation methods created (applied on either a map or a set of maps) in the current R console
are saved in the file.
If the file is a text file, it will include a line per marker with columns “set” (for the dataset name), “map”
(for the map name, ie. the chromosome name), “phys” (for the physical position of the marker), “gen” (for
the genetic position of the marker) and “vld” (indicating if the marker is valid or not). If interpolation
checkbox is checked), the file also contains a column per
methods are included (those for which the
interpolation (the column name is the interpolation method name) with the local recombination rate
computed for each marker. Functions used to build the interpolations are also saved as comments at the
beginning of the text file.
5.2
Exporting pictures
Maps can also be graphically exported in jpeg, png, pdf or eps formats. Only the currently diplayed map
is exported, with only the interpolations which are checked as “Displayed”. You can choose to export
either the Marey map (on the top), or the recombination rate display (on the bottom), or both.
5.3
Loading previous analyses
You may want to resume work on a dataset.
If the work was saved in a txt format, you can re-run interpolation methods using the R commands
previously used, which can be found at the top of the txt file.
If it has been saved in a rda format, the “Open” command loads all previously saved interpolations.
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